Joint Probabilistic Modeling of Wind Speed and Wind Direction for Wind Energy Analysis: A Case Study in Humansdorp and Noupoort

South Africa has great potential for considering wind energy as an alternative resource. The climatology allows for significant wind energy production. An accurate joint description of the wind speed (linear) and wind direction (circular) characteristics is important for wind farm development. In this paper, a bivariate class of flexible joint probability density functions of wind speed and wind direction for the use in wind energy analysis is presented. This joint model accounts for bimodality, skewness, and a dependency structure between the wind speed and wind direction. For the joint probabilistic description of the wind speed and wind direction, special cases of this bivariate class are evaluated, namely the semi-parametric Mobius model on the disc, the Mobius distribution on the disc, and the Beta type III Mobius distribution on the disc. These three special cases are applied to wind speed and wind direction data recorded every ten minutes at two locations in South Africa. Evaluation of the models is based on three different information criteria and normalized deviation. Overall, the semi-parametric model is superior to the parametric models based on the performance measures. The wind energy potential at the two locations is evaluated using the semi-parametric model.